EEA 2 residence card from tier 2 visa

[agnivab]

Dear Advisors
I have a question, which many colleagues consider bizarre. I am here in the UK on a tier 2 visa, working for the NHS as a surgeon since 2014. As far as my current visa is concerned, I have no issues with it. The current one expires in August 2018.And I am eligible to apply for ILR in Nov 2019. The hospital is more than happy to extend my tier 2 visa, and there is no foreseeable reason, why the home office would reject it. Till this, my situation is straightforward. Now comes the twist. My wife is a Portuguese citizen, and she is also an NHS worker. ( She is a senior nurse). We have a 6-month-old baby. Including the baby in the picture, the scenario gets a bit complicated. We both work shifts, which are generally 12 hours, includes day, night and weekends. We can't afford a full-time nanny, as the prices of a nanny, 7 days a week, would be astronomical, and no nursery is open over the weekends. Thus, the only other option is working part-time. I had a discussion with my HR, and I was informed that it is not an option, as it would breach the tier 2 rules of appropriate salary. Thus, weighing my priorities, I have decided to apply for an EEA 2 residence card, as an early ILR is less important than my baby.
I have 2 questions:-

1. Is it a stupid idea to change now to a different immigration pathway, considering the fact that, I have a stable job and a clean immigration history, my ILR application next year will not be turned down?

2. I have been with my partner for a bit more than 2 years, we were residing together, have joint bills, bank statements for the last 2 years, Did multiple trips together, have pictures, texts, emails and WhatsApp messages from last 2 years, which even the toughest caseworker would struggle to question its genuinity. We work at the same hospital (always did), we both are qualified professionals and have stable and respectable jobs, and most importantly we have a baby and are married, (which is endorsed in my passport and also authorised by the Portuguese embassy). For the ease of European travel, my baby has a Portuguese passport.
Considering my case, does your experienced eyes catch any flip side, which might be used against us, and a permit denied? Would I need to struggle again after Brexit?

I am not using a lawyer, and filling up the forms myself, as I believe I have enough supporting documentation, however, would you recommend using an immigration lawyer instead?
Regards and best wishes
AB